Problem: Simplify the following expression: $z = \dfrac{-9t^2 - 72t - 108}{t + 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ z =\dfrac{-9(t^2 + 8t + 12)}{t + 6} $ Then we factor the remaining polynomial: $t^2 + {8}t + {12} $ ${6} + {2} = {8}$ ${6} \times {2} = {12}$ $ (t + {6}) (t + {2}) $ This gives us a factored expression: $\dfrac{-9(t + {6}) (t + {2})}{t + 6}$ We can divide the numerator and denominator by $(t - 6)$ on condition that $t \neq -6$ Therefore $z = -9(t + 2); t \neq -6$